have a look at the papers below: 

Semiatin, S. L., and T. R. Bieler. "The effect of alpha platelet thickness on plastic flow during hot working of Ti–6Al–4V with a transformed microstructure." Acta materialia 49.17 (2001): 3565-3573.

Semiatin, S. L., and T. R. Bieler. "Effect of texture and slip mode on the anisotropy of plastic flow and flow softening during hot working of Ti-6Al-4V." Metallurgical and Materials Transactions A 32.7 (2001): 1787-1799.

Can you please tell us a bit more about what you meant by "contribution of alpha and beta volume"? 

Cheers, 

Ahmad

Thanks a lot Ahmad for your suggestion. But I am more worried about these constant at room temperature condition as the grain boundary strength is the function of temperature.  

And regarding the other part of my question: I wanted to know how much the alpha and beta phase individually contribute to strengthening of the two phase Titanium alloy at room temperature. If I know the relative contribution of alpha and beta phase of Titanium alloy. The total contribution due to these two phases to strengthening of the alloy can be obtained.

Ashish   

The paper below gives some data about Hall-Petch constants for Ti-64 at room temperature, which might be helpful for your research

[1] Zhang, M., J. Zhang, and D. L. McDowell. "Microstructure-based crystal plasticity modeling of cyclic deformation of Ti–6Al–4V." International Journal of Plasticity 23.8 (2007): 1328-1348.

In general, it is really hard to find a Hall-Petch equation for Ti-6Al-4V alloy containing two different phases (mostly lamellar with different orientations and thicknesses). Hall-Petch equation is commonly used for single-phase materials with equiaxed grains.

As for the second part of the question, I would suggest to have a look at the papers below:

[2] Gerday, Anne-Françoise, et al. "Numerical Modeling of Representative Cells of Ti-5553 Using Periodic Homogenization Technique." Computational plasticity X. Fundamentals and applications (2009).

[3] Weiss, I. and S.L. Semiatin, Thermomechanical processing of beta titanium alloys—an overview. Materials science & engineering. A, Structural materials: properties, microstructure and processing, 1998. 243(1): p. 46-65. 

According to ref. 2, the hardness of alpha is less than beta, while its ductility is much less than beta (i.e. alpha has got hcp crystal structure with limited slip systems), resulting in the development of stress concentration in beta [3]. So, contribution of each phase in strengthening cannot be determined easily as each phase has a different crystal structure, hardness and ductility. 

Regarding the volume fractions of each phase in the structure, we roughly calculated them once using the Pandat software and got the mass fractions of 10-20 wt.% and 80-90wt% for beta and alpha respectively, if I can remember correctly. You can calcualte them yourself. Even image analyzing or XRD can help calculate them.

Hope this helps.

Cheers   

Hello Ashish Kumar Saxena,

Did you succeed in finding the Hall-Petch Coefficient for Ti64?

Hi Olga,

Not exactly, the Hall Petch coefficient of Ti64 is not not able get it from literature..

Thank you for your prompt reply, So how did you solve this problem? You didn't take into account the effect of grain size on the yield strength for Ti64 at all, did you?